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Question : Directions: Three statements are given followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: All males are boys. Some teachers are boys. All students are teachers. Conclusions: I. Some boys are males. II. Some teachers are students. III. All males are students.
Option 1: All conclusions follow
Option 2: Only conclusions II and III follow
Option 3: Only conclusions I and II follow
Option 4: Only conclusions I and III follow
Correct Answer: Only conclusions I and II follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion I: Some boys are males – From the above Venn diagram, it is clear that some part of the circle of
Question : What is the effective annual rate of interest corresponding to a nominal rate of 10% per annum payable half-yearly?
Option 1: 10.25%
Option 2: 12.75%
Option 3: 9.25%
Option 4: 11.50%
Correct Answer: 10.25%
Solution : Rate, $\frac{R}{2}$ = 10% Time, $n$ = 1 year Let principal sum, $P$ be INR 100. When compounded half-yearly, Amount = $P(1+\frac{\frac{R}{2}}{200})^{2n}$ = $100(1+\frac{10}{200})^{2}$ = $100(\frac{21}{20})^{2}$ = $\frac{441}{4}$ = INR 110.25 Effective rate = $\frac{110.25-100}{100}×100$ = 10.25% Hence, the correct answer is 10.25%
Question : What is the value of $\frac{(a^2+b^2)(a-b)-(a-b)^3}{a^2b-ab^2}?$
Option 1: $0$
Option 2: $1$
Option 3: $–1$
Option 4: $2$
Correct Answer: $2$
Solution : Given: $\frac{(a^2+b^2)(a-b)-(a-b)^3}{a^2b-ab^2}$ = $\frac{(a-b)(a^2+b^2-(a-b)^2)}{ab(a-b)}$ = $\frac{a^2+b^2-a^2+2ab-b^2}{ab}$ = $\frac{2ab}{ab}$ = $2$ Hence, the correct answer is $2$.
Question : What is the value of $3 \tan 20° \tan 45°\tan 70°$?
Option 1: 2
Option 2: 3
Option 3: 1.5
Option 4: 4
Correct Answer: 3
Solution : $3 \tan 20°\tan 45° \tan70°$ $= 3 \tan 20°\tan 45° \tan (90° - 20°)$ [Using $\tan \theta = \cot (90° - \theta)$] $= 3 \tan 20°\tan 45°\cot 20°$ $= 3 \times \tan 45°$ $= 3 \times 1$ $= 3$ Hence, the correct answer is 3.
Question : Evaluate the following:$\sqrt{2+\sqrt{2+\sqrt{2+2\cos8\theta}}}$
Option 1: $2 \cos \theta$
Option 2: $2 \cos 2 \theta$
Option 3: $\sin 2 \theta$
Option 4: $\cos 2 \theta$
Correct Answer: $2 \cos \theta$
Solution : We know, $\cos2\theta= 2\cos^2\theta-1$ ⇒ $\cos2\theta+1= 2\cos^2\theta$ Putting $\theta=4\theta$ on both sides, we get $\therefore \cos8\theta+1=2\cos^24\theta$ Given, $\sqrt{2+\sqrt{2+\sqrt{2+2\cos8\theta}}}$ = $\sqrt{2+\sqrt{2+\sqrt{2(1+\cos8\theta)}}}$ = $\sqrt{2+\sqrt{2+\sqrt{2(2\cos^24\theta)}}}$ = $\sqrt{2+\sqrt{2+2\cos4\theta}}$ = $\sqrt{2+\sqrt{2(1+\cos4\theta)}}$ = $\sqrt{2+\sqrt{2(2\cos^22\theta))}}$ = $\sqrt{2+2\cos2\theta}$ = $\sqrt{2(1+\cos2\theta)}$ = $\sqrt{2(2\cos^2\theta)}$ = $2 \cos \theta$ Hence, the correct answer is
Question : Which of the following constitutional amendment acts made the right to education a fundamental right under Article 21A of the Indian constitution?
Option 1: 91st Amendment Act, 2003
Option 2: 86th Amendment Act, 2002
Option 3: 89th Amendment Act, 2003
Option 4: 19th Amendment Act, 1966
Correct Answer: 86th Amendment Act, 2002
Solution : The correct answer is the 86th Amendment Act, of 2002.
The 86th Amendment Act, 2002 came during the Atal Bihari Vajpayee government. This act makes it obligatory on the part of the government to ensure admission, attendance, and completion of elementary
Question : Vembanad Lake is located in which of the following states?
Option 1: Andhra Pradesh
Option 2: Kerala
Option 3: Tamil Nadu
Option 4: Karnataka
Correct Answer: Kerala
Solution : The correct option is Kerala.
Vembanad Lake is located in the state of Kerala. It is the longest lake in India and the largest lake in the state of Kerala. Vembanad is a brackish lagoon. It is the longest lake in India and one
Question : A sum of Rs. 730 was divided among A, B and C in such a way that if A gets Rs. 3, then B gets Rs. 4. And if B gets Rs. 3.50, then C gets Rs. 3. The share of B exceeds that of C by:
Option 1: Rs. 30
Option 2: Rs. 40
Option 3: Rs. 70
Option 4: Rs. 210
Correct Answer: Rs. 40
Solution : Given: A sum of Rs. 730 was divided among A, B and C in such a way that if A gets Rs. 3, then B gets Rs. 4. And if B gets Rs. 3.50, then C gets Rs. 3. So, A : B =
Question : In the following question, out of the given four alternatives, select the alternative which best expresses the meaning of the Idiom/Phrase.
To strain every nerve
Option 1: To go for physiotherapy
Option 2: To manipulate someone in the best way
Option 3: To claim something
Option 4: To make a great effort
Correct Answer: To make a great effort
Solution : The correct choice is the fourth option.
Explanation
The idiom to strain every nerve means to put in maximum effort or to make an intense and determined attempt to achieve something.
Therefore, the correct meaning of the idiom is to make
Question : Find the part of the given sentence that has an error in it. If there is no error, choose ‘No Error’. You will get a discount on this products, if you buy one more outfit.
Option 1: No Error
Option 2: on this products, if
Option 3: You will get a discount
Option 4: you buy one more outfit
Correct Answer: on this products, if
Solution : The error lies in the second option.
The error is in the phrase, on this products. The correct form is on these products because products is plural. Products is a plural form, so it should take the plural demonstrative pronoun, these
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